Answer :

A. Angular speed is the rate of change of angular position of an object w.r.t. time.

Dimensions of dθ =[M0L0T0]

Dimensions of dt = [T]

Dimensions of ω = .

B. Angular acceleration is the rate of change of angular speed w.r.t time.

Dimensions of dω =

Dimensions of dt = [T]

Dimensions of =

C. Torque is the rotational effect of a linear force. It is the turning effect when a force is applied on a body that can rotate.

Torque(T) = Force(F) × distance from axis (r)

Dimensions of F = [MLT-2]

Dimensions of r = [L1]

Dimensions of T = [MLT-2] × [L1] = [ML2T-2]

D. Moment of inertia is defined as the inertia of a rotating body w.r.t. its axis of rotation.

Moment of inertia (I) = mass of body (m) × square of distance from axis(r2)

Dimensions of m = [M]

Dimensions of r2 = [L2]

Dimensions of I = [M] × [L2] = [ML2]

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